For the past six months, the jobless rate had clung to 4.1 percent, the longest it had gone without budging since the late 1960s. (The record to beat: nine months.) The streak defied the expectations of economists, who said the nation's prolonged hiring blitz was bound to drive the figure down.

"It’s an exciting headline for the worker,” said Josh Wright, Chief Economist at iCIMS, a software company. “A real Goldilocks number, with job growth being great.”

But pay stayed flat, so the Federal Reserve won’t likely feel pressure to raise rates before June. In other words, Wright said, the markets should respond favorably.

“What we’re seeing here is steadiness,” he said.

Most of the April hiring happened in professional and business services, which grew by 54,000 jobs. Employment in manufacturing jumped by 24,000, mostly in the durable goods area. Health care added 24,000 positions and mining hopped by 7,000.

If the expansion further gains steam, analysts at the Fed said the unemployment rate could reach 3.7 percent this year, a figure not seen since 1969.

“The longer the economy burns hot, the more workers are in the driver's seat negotiating with companies,” said Andrew Chamberlain, chief economist at Glassdoor, a jobs site.

That should bring “not spectacular, but slowly building” raises as employers struggle to fill vacancies.

A demographic shift partly explains why employers are having trouble finding talent. Baby boomers, which today represent a third of the workforce, are retiring in droves, said Joe Brusuelas, chief economist at RSM, an international consulting firm. Younger workers aren’t replacing them.

And although millennials constitute 35 percent of America’s workers, they’re more likely than previous generations to have attended college — and less likely to have picked up a trade at vocational school. They're less likely to take jobs in construction and manufacturing. (Employers in both sectors have turned to raises and high school recruiting to shrink their gaps.)

Companies across the country have already made adjustments to account for the dearth of applicants. More employers, including blue-collar firms, are offering larger bonuses (which do not show up in the government’s wage data). They’re ramping up on-the-job training, which economists say will play a larger role in the economy as technology advances.

Although some businesses say the lack of workers thwarts their growth, the U.S. has experienced a steady hiring streak this year, adding an average of 202,000 new positions each month. (Progress dipped in March, but economists blamed the unusually snowy weather.)

Becky Barr, head of data insights at Adzuna.com, a jobs site, said health care is driving much of the trend, with openings up 37 percent in the past four months (268,610). Government vacancies, according to her analysis, have also been on the rise since February (40,000).